# Distance from Point to Plane Calculator

URL: https://speedycalculator.com/calculators/math/distance-from-point-to-plane/
Last updated: 2026-10-30

> The point-to-plane distance calculator finds the shortest distance from a point (a, b, c) to a plane given in standard form Ax + By + Cz + D = 0 or by a normal vector and a point.

## Inputs

- Point a (x)
- Point b (y)
- Point c (z)
- How is your plane given?
- A
- B
- C
- D
- Point on plane x
- Point on plane y
- Point on plane z

## Results

- Distance from point to plane
- Signed distance
- Length of the normal |n|

## Formula

```
L = |A·a + B·b + C·c + D| ÷ √(A² + B² + C²)
```

## Explanation

The shortest distance from a point to a plane is measured along the plane's normal. It is used in 3D graphics (clipping and collision), robotics, surveying and crystallography.

### How to use the Distance from Point to Plane Calculator

- **Point a (x)**
- **Point b (y)**
- **Point c (z)**
- **How is your plane given?**
- **A**
- **B**
- **C**
- **D**
- **Point on plane x**
- **Point on plane y**
- **Point on plane z**

Results update as you type, and everything is calculated in your browser.

### How it works

The point is substituted into the plane equation and the result divided by the length of the normal vector. With a normal and a point, D is computed first.

### Inputs explained

FieldWhat to enterPoint a (x)A numberPoint b (y)A numberPoint c (z)A numberHow is your plane given?Choose one: Standard form Ax + By + Cz + D = 0, Normal vector and a point on the planeAA numberBA numberCA numberDA numberPoint on plane xA numberPoint on plane yA numberPoint on plane zA number

### Example values

How the main result changes when **Point a** changes and everything else stays at the example values above:

Point a (x)Distance from point to plane0.50.33330.750.510.66671.250.83331.5121.3333

## Worked example

Inputs — Point a (x): 1; Point b (y): 2; Point c (z): 3; How is your plane given?: Standard form Ax + By + Cz + D = 0; A: 2; B: -1; C: 2; D: -4.

Results — **Distance from point to plane = 0.66666667**; Signed distance = 0.66666667; Length of the normal |n| = 3.

## Key terms

- **Normal vector**: A vector perpendicular to a plane.

## FAQ

**Why divide by √(A² + B² + C²)?**
To turn the plane equation value into a true distance along a unit normal.

**What does the sign of the signed distance mean?**
Which side of the plane the point is on.

**What if the distance is zero?**
The point lies on the plane.

**How do I get D from a normal and a point?**
D = −(A·x₀ + B·y₀ + C·z₀).


## Sources

- [OpenStax – Calculus Volume 3](https://openstax.org/details/books/calculus-volume-3)
- [Wolfram MathWorld – Point-plane distance](https://mathworld.wolfram.com/Point-PlaneDistance.html)